Dataset Information

Partial likelihood estimation of isotonic proportional hazards models.

ABSTRACT: We consider the estimation of the semiparametric proportional hazards model with an unspecified baseline hazard function where the effect of a continuous covariate is assumed to be monotone. Previous work on nonparametric maximum likelihood estimation for isotonic proportional hazard regression with right-censored data is computationally intensive, lacks theoretical justification, and may be prohibitive in large samples. In this paper, partial likelihood estimation is studied. An iterative quadratic programming method is considered, which has performed well with likelihoods for isotonic parametric regression models. However, the iterative quadratic programming method for the partial likelihood cannot be implemented using standard pool-adjacent-violators techniques, increasing the computational burden and numerical instability. The iterative convex minorant algorithm which uses pool-adjacent-violators techniques has also been shown to perform well in related parametric likelihood set-ups, but evidences computational difficulties under the proportional hazards model. An alternative pseudo-iterative convex minorant algorithm is proposed which exploits the pool-adjacent-violators techniques, is theoretically justified, and exhibits computational stability. A separate estimator of the baseline hazard function is provided. The algorithms are extended to models with time-dependent covariates. Simulation studies demonstrate that the pseudo-iterative convex minorant algorithm may yield orders-of-magnitude reduction in computing time relative to the iterative quadratic programming method and the iterative convex minorant algorithm, with moderate reductions in the bias and variance of the estimators. Analysis of data from a recent HIV prevention study illustrates the practical utility of the isotonic methodology in estimating nonlinear, monotonic covariate effects.

SUBMITTER: Chung Y

PROVIDER: S-EPMC5969539 | biostudies-literature | 2018 Mar

REPOSITORIES: biostudies-literature

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Partial likelihood estimation of isotonic proportional hazards models.

Chung Yunro Y Ivanova Anastasia A Hudgens Michael G MG Fine Jason P JP

Biometrika 20171205 1

We consider the estimation of the semiparametric proportional hazards model with an unspecified baseline hazard function where the effect of a continuous covariate is assumed to be monotone. Previous work on nonparametric maximum likelihood estimation for isotonic proportional hazard regression with right-censored data is computationally intensive, lacks theoretical justification, and may be prohibitive in large samples. In this paper, partial likelihood estimation is studied. An iterative quadr ...[more]

PMID: 29808076

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Project description:BackgroundThe successful identification of breast cancer (BRCA) prognostic biomarkers is essential for the strategic interference of BRCA patients. Recently, various methods have been proposed for exploring a small prognostic gene set that can distinguish the high-risk group from the low-risk group.MethodsRegularized Cox proportional hazards (RCPH) models were proposed to discover prognostic biomarkers of BRCA from gene expression data. Firstly, the maximum connected network with 1142 genes by mapping 956 differentially expressed genes (DEGs) and 677 previously BRCA-related genes into the gene regulatory network (GRN) was constructed. Then, the 72 union genes of the four feature gene sets identified by Lasso-RCPH, Enet-RCPH, [Formula: see text]-RCPH and SCAD-RCPH models were recognized as the robust prognostic biomarkers. These biomarkers were validated by literature checks, BRCA-specific GRN and functional enrichment analysis. Finally, an index of prognostic risk score (PRS) for BRCA was established based on univariate and multivariate Cox regression analysis. Survival analysis was performed to investigate the PRS on 1080 BRCA patients from the internal validation. Particularly, the nomogram was constructed to express the relationship between PRS and other clinical information on the discovery dataset. The PRS was also verified on 1848 BRCA patients of ten external validation datasets or collected cohorts.ResultsThe nomogram highlighted that the importance of PRS in guiding significance for the prognosis of BRCA patients. In addition, the PRS of 301 normal samples and 306 tumor samples from five independent datasets showed that it is significantly higher in tumors than in normal tissues ([Formula: see text]). The protein expression profiles of the three genes, i.e., ADRB1, SAV1 and TSPAN14, involved in the PRS model demonstrated that the latter two genes are more strongly stained in tumor specimens. More importantly, external validation illustrated that the high-risk group has worse survival than the low-risk group ([Formula: see text]) in both internal and external validations.ConclusionsThe proposed pipelines of detecting and validating prognostic biomarker genes for BRCA are effective and efficient. Moreover, the proposed PRS is very promising as an important indicator for judging the prognosis of BRCA patients.

Dataset Information

Partial likelihood estimation of isotonic proportional hazards models.

Publications

Partial likelihood estimation of isotonic proportional hazards models.

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